Cannot select certain vertices
Click with the other side of the Mouse



Press 
a
 one or twice so that nothing is selected and the image looks dim not bright.  Its a toggle.

Then Click Only



Then use
b
for box select and you should see a difference.

My opinion is that everything is selected in you original question.

You can also press 
W
then select subdivide to have more variation in your selection.

Perhaps you  already know this.